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The sequence $4 ; 9 ; x ; 37 ; ... $ is a quadratic sequence.

  1. Calculate $x$
  2. Hence, or otherwise, determine the nth term of the sequence
in Grade 12 Maths by Diamond (47.6k points) | 287 views

1 Answer

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1. 1st difference= 5,x-9,37-x,...

    2nd difference= x-9-5, 37-x-(x-9),...

since 2nd difference is constant,

  x-9-5 = 37-x-(x-9)


     3x= 60


2.  2a= x-9-5 = 20-9-5= 6

     2a= 6

    a= 3


       b= 5-3(3)

         b= -4

a+b+c= 4

          c= 4-3-(-4)

             c= 5

Therefore nth term = 3n^2 -4n +5
by Diamond (38.0k points)
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